Strange liquid in glass and thick glass behavior
Finally, I tried several things and I got a better result by reworking lighting and trying a new camera angle. I closed the space where my flask is, added windows, added a ceiling, and added a few area lights at the top. I also tweaked my colors and absorption values. I also separated the interface meshes (now, they aren't connected, but still in the same object).

Here is my result



And here is my CuSO4ToAir material (the only difference with the CuSO4ToGlass is the IOR)



I will mark this answer as solution, but I am still listening to a better solution if you have.